In the pharmaceutical industry, the adoption of quality by design (QbD) has been an evolving process. QbD refers to a systematic process to build quality into a product from the inception to the final output. Specifically, QbD refers to the level of effectiveness of a design function in determining a product's operational requirements (and their incorporation into design requirements) that can be converted into a finished product in a production process. This is often referred to as a design space, which is the multidimensional combination and interaction of input factors (e.g., material attributes) that have been demonstrated to provide assurance of quality. For example, for a manufacturing process a design space is the set of possible designs and design parameters (input factors) that meet a specific product requirement (one or more output responses). Exploring a design space requires evaluating the various design options possible with a given technology and optimizing the input factors and output responses with respect to specific constraints (e.g., power, cost, mixture design).
In the semiconductor device manufacturing industry, device manufacturers have transitioned to more closely toleranced process and materials specifications by relying on process tool manufacturers to design better and/or faster process and hardware configurations. However, as device geometries shrink to the nanometer scale, complexity in manufacturing processes increases, and process and material specifications become more difficult to meet.
A typical process tool used in current semiconductor manufacturing can be described by a set of several thousand process variables. The variables are generally related to physical parameters of the manufacturing process and/or tools used in the manufacturing process. In some cases, of these several thousand variables, several hundred variables are dynamic (e.g., changing in time during the manufacturing process or between manufacturing processes). The dynamic variables (e.g., gas flow, gas pressure, delivered power, current, voltage, and temperature) change based on various operating factors (e.g., a specific processing recipe, the particular step or series of steps in the overall sequence of processing steps, errors and faults that occur during the manufacturing process or changes (e.g., referred to as “drift”) in parameter values based on use of a particular tool or chamber).
Operators can control the manufacturing process by, for example, changing input factors, which are variables that influence the production process. For each manufacturing process, output response values (e.g., temperature, yield, quality attributes) can be measured that depend on input factors. Experiments can be performed for the particular manufacturing process to determine what combinations of input factor values result in acceptable output response values.
A Design of Experiment (DOE) method is a structured, organized method for determining the relationship between input factors for a process (e.g., a manufacturing process, mixture design) and the output responses of that process. The DOE method can quantify indeterminate measurements of input factors and interactions between the input factors statistically through observing the results of methodical changes of the input factors. If there are operational criteria associated with the process, output response values are measured for different combinations of input factors to determine if the operational criteria are satisfied for each combination.
Exploring a design space requires manually evaluating the various design options possible based on any operational criteria. There is no way to automatically provide for acceptable regions of variability of each input factor, or to predict result regions. The analysis process is further complicated when several demands on the output responses have to be met at the same time with different types of constraints. Further, it would be desirable for graphical methods to display design spaces in a way that can be easily analyzed and interpreted by an operator.